Finite Group Databasebeta

← #14682493

Subgroups — #14682493

Order 2816.

1354 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622542C211yesmaximal, characteristic
2C2×#10622259C212yesmaximal
3#13066879C212yesmaximal
4#13066871C212yesmaximal
5#13066868C212yesmaximal
6#13066851C212yesmaximal
7#13066848C212yesmaximal
8#13066843C211yesmaximal, characteristic
9C11×C4⋊#95C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×C4×Dic11C2212yes—
17C2×C11×#95C2212yes—
18C2×C11×#95C2211yescharacteristic
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2211yescharacteristic
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622542C418yescomplemented
32#10622259—28no—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×Dic22—42no—
43C22×Dic22—42no—
44C22×Dic22C2×C414yes—
45C22×Dic22D414yes—
46C22×Dic22Q814yes—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4—42no—
50C2×C42×C11—42no—
51C2×C42×C11C2×C414yes—
52C2×C4⋊Dic11—42no—
53C2×C4⋊Dic11C2×C414yes—
54C2×Dic11⋊C4—24no—
55C2×Dic11⋊C4—24no—
56C2×Dic11⋊C4—42no—
57C2×Dic11⋊C4—42no—
58C2×Dic11⋊C4—42no—
59C2×Dic11⋊C4—42no—
60C2×C4×Dic11—24no—
61C2×C4×Dic11—42no—
62C2×C4×Dic11—42no—
63C11×#95—24no—
64C11×#95—41no—
65C11×#95—41no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C11⋊#95—22no—
69C11⋊#95—24no—
70C11⋊#95—24no—
71C11⋊#95—42no—
72C11⋊#95—42no—
73C11⋊#95—42no—
74C11⋊#95C2×C418yes—
75C11⋊#95C2×C418yes—
76C11⋊#95Q814yescomplemented
77#14466—111nomaximal, Sylow
78C24×C11C2411yescharacteristic
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×Q812yes—
105C22×C4×C11C2×Q812yes—
106C22×C4×C11#4114yes—
107C22×C4×C11#4112yes—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11C22×C414yes—
132C22×Dic11C22×C414yes—
133C22×Dic11C2×D414yes—
134C22×Dic11C2×Q814yes—
135C22×Dic11C2×Q814yes—
136C2×Dic22—44no—
137C2×Dic22—44no—
138C2×Dic22—48no—
139C2×Dic22—48no—
140C2×Dic22C4⋊C4116yescomplemented
141C11×C4⋊C4—48no—
142C42×C11—44no—
143C4⋊Dic11—44no—
144Dic11⋊C4—48no—
145Dic11⋊C4—48no—
146C4×Dic11—48no—
147C2×#391—111no—
148C2×#391—112no—
149#1444—112no—
150#1442—112no—
151#1441—112no—
152#1436—112no—
153#1436—112no—
154C4⋊#95D1111yescharacteristic
155#1434—111no—
156C23×C11C23×C411yescharacteristic
157C23×C11C22×D411yescharacteristic
158C23×C11C22×Q811yescharacteristic
159C23×C11C22×Q811yescharacteristic
160C23×C11C2×#4112yes—
161C23×C11C2×#4111yescharacteristic
162C23×C11H(5,𝔽2)12yes—
163C23×C11H(5,𝔽2)11yescharacteristic
164C23×C11H(5,𝔽2)12yes—
165C23×C112−1+411yescharacteristic
166C23×C112−1+412yes—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C4⋊C414yes—
195C2×C4×C11C4×Q814yes—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11C2×C4⋊C418yes—
224Dic22—416no—
225C23×Q8—111no—
226C22×C4⋊C4—111no—
227C22×C4⋊C4—112no—
228C22×C4⋊C4—112no—
229C22×C4⋊C4C2×D1112yes—
230C22×C42—112no—
231C22×C42C2×D1111yescharacteristic
232#391—118no—
233#391—228no—
234C2×#95—111no—
235C2×#95—112no—
236C2×#95—112no—
237C2×#95—112no—
238C2×#95—111no—
239C2×#95—112no—
240C2×#95—112no—
241C2×#95—112no—
242C2×#95—112no—
243C2×#95—112no—
244C2×#95—112no—
245C2×#95C2×D1112yes—
246C2×#95C2×D1111yescharacteristic
247C2×#95C2×D1111yescharacteristic
248C22×C11C22×C4⋊C411yescharacteristic
249C22×C11C2×C4×Q811yescharacteristic
250C22×C11C4×#4111yescharacteristic
251C22×C11#51811yescharacteristic
252C22×C11#51811yescharacteristic
253C22×C11#51911yescharacteristic
254C22×C11#52011yescharacteristic
255C22×C11#53412yes—
256C22×C11#53812yes—
257C22×C11#54212yes—
258C22×C11#54212yes—
259C22×C11#54312yes—
260C22×C11#54412yes—
261C22×C11#54812yes—
262C22×C11D4×Q811yescharacteristic
263C22×C11#55011yescharacteristic
264C22×C11#55112yes—
265C22×C11#55412yes—
266C22×C11#55711yescharacteristic
267C22×C11#55712yes—
268C22×C11Q8211yescharacteristic
269C22×C11#56212yes—
270C22×C11#56312yes—
271C4×C11—24no—
272C4×C11—24no—
273C4×C11—42no—
274C4×C11—44no—
275C4×C11—82no—
276Dic11—28no—
277Dic11—44no—
278Dic11—44no—
279Dic11—82no—
280C22×Q8—114no—
281C22×Q8—114no—
282C22×Q8—114no—
283C22×Q8—442no—
284C22×Q8—442no—
285C23×C4—112no—
286C23×C4—112no—
287C23×C4—112no—
288C23×C4—112no—
289C23×C4C22×D1112yes—
290C23×C4C22×D1111yescharacteristic
291C23×C4C22×D1112yes—
292C23×C4C22×D1111yescharacteristic
293C23×C4C22×D1111yescharacteristic
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—114no—
298C2×C4⋊C4—224no—
299C2×C4⋊C4—224no—
300C2×C4⋊C4—442no—
301C2×C4⋊C4—442no—
302C2×C4⋊C4—442no—
303C2×C4⋊C4—442no—
304C2×C4⋊C4—442no—
305C2×C42—42no—
306C2×C42—224no—
307C2×C42—442no—
308C2×C42—442no—
309C2×C42C4×D1114yes—
310#95—24no—
311#95—41no—
312#95—41no—
313#95—118no—
314#95—118no—
315#95—114no—
316#95—224no—
317#95—224no—
318#95—224no—
319#95—224no—
320#95—222no—
321#95—442no—
322#95—442no—
323#95—442no—
324C2×C11#231511yescharacteristic
325C2×C11#233111yescharacteristic
326C2×C11#233711yescharacteristic
327C2×C11Q8×C4⋊C411yescharacteristic
328C2×C11#235111yescharacteristic
329C2×C11#236811yescharacteristic
330C2×C11#237811yescharacteristic
331C2×C11#272912yes—
332C2×C11#273012yes—
333C2×C11#279912yes—
334C2×C11#280612yes—
335C24C23×D1111yescharacteristic
336C2×Q8—1116no—
337C2×Q8—444no—
338C2×Q8—444no—
339C2×Q8—448no—
340C2×Q8—448no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—114no—
363C22×C4—114no—
364C22×C4—114no—
365C22×C4—114no—
366C22×C4—114no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4C2×C4×D1112yes—
391C22×C4C2×C4×D1112yes—
392C22×C4C2×C4×D1112yes—
393C22×C4#433914yes—
394C22×C4D4×D1112yes—
395C22×C4#434112yes—
396C22×C4Q8×D1112yes—
397C22×C4Q8×D1112yes—
398C4⋊C4—48no—
399C4⋊C4—444no—
400C4⋊C4—448no—
401C4⋊C4—448no—
402C42—44no—
403C42—448no—
404C11#1446611yescharacteristic, complemented, Sylow
405C23C22×C4×D1111yescharacteristic
406C23C2×#433912yes—
407C23C2×D4×D1111yescharacteristic
408C23C2×#434111yescharacteristic
409C23#6703711yescharacteristic
410C23#6703712yes—
411C23C2×Q8×D1111yescharacteristic
412C23C2×Q8×D1111yescharacteristic
413C23#6704011yescharacteristic
414C23#6704212yes—
415C23#6704312yes—
416Q8—4416no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—118no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—224no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—224no—
451C2×C4—224no—
452C2×C4—224no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4#6694014yes—
473C2×C4C4⋊C4×D1114yes—
474C22C4×#433911yescharacteristic
475C22#1062301711yescharacteristic
476C22#1062302612yes—
477C22C2×#6694011yescharacteristic
478C22C2×C4⋊C4×D1111yescharacteristic
479C22#1062303511yescharacteristic
480C22#1062304212yes—
481C22#1062304711yescharacteristic
482C22#1062305211yescharacteristic
483C22#1062308312yes—
484C22#1062309112yes—
485C22#1062309812yes—
486C22#1062311312yes—
487C22#1062313612yes—
488C22#1062315212yes—
489C22#1062316512yes—
490C22#1062317712yes—
491C22#1062321312yes—
492C22#1062322012yes—
493C22#1062324911yescharacteristic
494C22#1062325211yescharacteristic
495C22#1062325311yescharacteristic
496C22#1062325811yescharacteristic
497C4—24no—
498C4—24no—
499C4—44no—
500C4—42no—
501C4—82no—
502C4—228no—
503C4—444no—
504C4—444no—
505C4—882no—
506C2#1307122911yescharacteristic
507C2#1307136211yescharacteristic
508C2#1307142911yescharacteristic
509C2#1307152811yescharacteristic
510C2#1307153611yescharacteristic
511C2#1307169611yescharacteristic
512C2#1307177911yescharacteristic
513C2#1307559312yes—
514C2#1307560812yes—
515C2#1307649712yes—
516C2#1307657312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4⋊#95D11
hypocenterC11#14466
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
31. #10622542C4semidirect
76. C11⋊#95Q8semidirect
140. C2×Dic22C4⋊C4semidirect
404. C11#14466semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106225422
C2×#106222592
#130668792
#130668712
#130668682
#130668512
#130668482
#130668432
C11×C4⋊#952
#1446611